thermal energy series

1. MIT Course 16
Fall 2002
Thermal Energy
16.050
Prof. Z. S. Spakovszky
Notes by E.M. Greitzer
Z. S. Spakovszky

2. Table of Contents
PART 0 - PRELUDE: REVIEW OF “UNIFIED ENGINEERING THERMODYNAMICS”
0.1 What it's all about 0-1
0.2 Definitions and fundamentals ideas of thermodynamics 0-1
0.3 Review of thermodynamics concepts 0-2
PART 1 - THE SECOND LAW OF THERMODYNAMICS
1.A- Background to the Second Law of Thermodynamics
1.A.1 Some Properties of Engineering Cycles: Work and Efficiency 1A-1
1.A.2 Carnot Cycles 1A-3
1.A.3 Brayton Cycles (or Joule Cycles): The Power Cycle for a Gas Turbine Jet 1A-5
Engine
1.A.4 Gas Turbine Technology and Thermodynamics 1A-8
1.A.5 Refrigerators and heat pumps 1A-11
1.A.6 Reversibility and Irreversibility in Natural Processes 1A-12
1.A.7 Difference between Free Expansion of a Gas and Reversible Isothermal 1A-14
Expansion
1.A.8 Features of reversible Processes 1A-16
1.B The Second Law of Thermodynamics
1.B.1 Concept and Statements of the Second Law 1B-1
1.B.2 Axiomatic statements of the Laws of Thermodynamics 1B-3
1.B.3 Combined First and Second Law Expressions 1B-5
1.B.4 Entropy Changes in an Ideal Gas 1B-6
1.B.5 Calculation of Entropy Change in Some Basic Processes 1B-7
1.C Applications of the Second Law
1.C.1 Limitations on the Work that Can be Supplied by a Heat Engine 1C-1
1.C.2 The thermodynamic Temperature Scale 1C-3
1.C.3 Representation of Thermodynamic Processes in T-s coordinates 1C-4
1.C.4 Brayton Cycle in T-s coordinates 1C-5
1.C.5 Irreversibility, Entropy Changes, and Lost Work 1C-8
1.C.6 Entropy and Unavailable Energy 1C-11
1.C.7 Examples of Lost Work in Engineering Processes 1C-14
1.C.8 Some Overall Comments on Entropy, Reversible and Irreversible Processes 1C-23
1.D Interpretation of Entropy on the Microscopic Scale - The Connection between Randomness and
Entropy
1.D.1 Entropy Change in Mixing of Two ideal Gases 1D-1
1.D.2 Microscopic and Macroscopic Descriptions of a System 1D-2
1.D.3 A Statistical Definition of Entropy 1D-3
1.D.4 Connection between the Statistical Definition of Entropy and Randomness 1D-5

3. 1.D.5 Numerical Example of the Approach to the Equilibrium Distribution 1D-6
1.D.6 Summary and Conclusions 1D-11
PART 2 - POWER AND PROPULSION CYCLES
2.A Gas Power and Propulsion Cycles
2.A.1 The Internal Combustion Engine (Otto Cycle) 2A-1
2.A.2 Diesel Cycle 2A-4
2.A.3 Brayton Cycle 2A-5
2.A.4 Brayton Cycle for Jet Propulsion: the Ideal Ramjet 2A-6
2.A.5 The Breguet Range Equation 2A-8
2.A.6 Performance of the Ideal Ramjet 2A-11
2.A.7 Effect of departures from Ideal Behavior 2A-14
2.B Power Cycles with two-Phase media
2.B.1Behavior of Two-Phase Systems 2B-1
2.B.2 Work and Heat Transfer with Two-Phase Media 2B-5
2.B.3 The Carnot Cycle as a Two-Phase Power Cycle 2B-8
2.B.4 Rankine Power Cycles 2B-13
2.B.5 Enhancements of, and Effect of Design Parameters on Rankine Cycles 2B-15
2.B.6 Combined Cycles in Stationary Gas Turbine for Power Production 2B-19
2.B.7 Some Overall Comments on Thermodynamic Cycles 2B-21
2.C Introduction to Thermochemistry
2.C.1 Fuels 2C-1
2.C.2 Fuel-Air Ratio 2C-2
2.C.3 Enthalpy of Formation 2C-2
2.C.4 First Law analysis of Reacting systems 2C-4
2.C.5 Adiabatic Flame Temperature 2C-7
PART 3 - INTRODUCTION TO ENGINEERING HEAT TRANSFER
1.0 Heat Transfer Modes.......................................................................................................... HT-5
2.0 Conduction Heat Transfer .................................................................................................. HT-5
2.1 Steady-State One-Dimensional Conduction.................................................................... HT-8
2.2 Thermal Resistance Circuits ..........................................................................................HT-10
2.3 Steady Quasi-One-Dimensional Heat Flow in Non-Planar Geometry ........................... HT-14
3.0 Convective Heat Transfer..................................................................................................HT-18
3.1 The Reynolds Analogy..................................................................................................HT-19
3.2 Combined Conduction and Convection .........................................................................HT-24
3.3 Dimensionless Numbers and Analysis of Results ..........................................................HT-29
4.0 Temperature Distributions in the Presence of Heat Sources...............................................HT-32
5.0 Heat Transfer From a Fin ..................................................................................................HT-35
6.0 Transient Heat Transfer (Convective Cooling or Heating) .................................................HT-40
7.0 Some Considerations in Modeling Complex Physical Processes........................................HT-42
8.0 Heat Exchangers ...............................................................................................................HT-43

4. 8.1 Efficiency of a Counterflow Heat Exchanger.................................................................HT-50
9.0 Radiation Heat Transfer (Heat transfer by thermal radiation).............................................HT-52
9.1 Ideal Radiators ..............................................................................................................HT-53
9.2 Kirchhoff's Law and "Real Bodies" ...............................................................................HT-55
9.3 Radiation Heat Transfer Between Planar Surfaces .........................................................HT-55
9.4 Radiation Heat Transfer Between Black Surfaces of Arbitrary Geometry ......................HT-60

5. ACKNOWLEDGEMENT
Preparation of these notes has benefited greatly from the expertise of a number of individuals,
and we are pleased to acknowledge this help. Jessica Townsend, Vincent Blateau, Isabel
Pauwels, and David Milanes, the successive Teaching Assistants in this core department course,
provided ideas, corrected errors, inserted “Muddy Points”, supplied the index, and in general,
created a much more readable document. Any errors that remain, or lack of readability, are thus
the sole responsibility of the authors. We also appreciate the work of Diana Park and Robin
Palazzolo, who contributed greatly to the editing and graphics. Finally, we are grateful to have
had the opportunity to discuss some of the material with Professor Frank Marble of Caltech,
whose understanding, insight, and ability to describe thermofluids concepts provide a model of
how to address important technical problems.